Spieth struggled on the opening two days of the tournament but managed to overcome that as he carded a four-under-par 67 to move up to second.
The 22-year-old now sits just three shots adrift of home favourite and leader Matt Jones, despite dropping three strokes over the opening four holes.
The American recovered well as he hit six birdies and an eagle on the 17th to end the day on a high as he looks to defend his title.
Spieth said: "It was obviously quite a fortunate break on the 17th to go in.
"I struck it nicely, there's not too much room to land it up there. But today was one of the great fightbacks I've had. I fought hard.
"And now I'm well in contention and in the last group, whether it's three or four behind, it's a lot better than I'd thought it would be after four holes.
"When I finished my round I thought I'd be tied or one back but either way it's a lot better than I thought it was going to be."